iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://pubmed.ncbi.nlm.nih.gov/20866299
Spectral properties of the Google matrix of the World Wide Web and other directed networks - PubMed Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2010 May;81(5 Pt 2):056109.
doi: 10.1103/PhysRevE.81.056109. Epub 2010 May 25.

Spectral properties of the Google matrix of the World Wide Web and other directed networks

Bertrand Georgeot  1 , Olivier Giraud, Dima L Shepelyansky
Affiliations

Spectral properties of the Google matrix of the World Wide Web and other directed networks

Bertrand Georgeot et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May.

Abstract

We study numerically the spectrum and eigenstate properties of the Google matrix of various examples of directed networks such as vocabulary networks of dictionaries and university World Wide Web networks. The spectra have gapless structure in the vicinity of the maximal eigenvalue for Google damping parameter α equal to unity. The vocabulary networks have relatively homogeneous spectral density, while university networks have pronounced spectral structures which change from one university to another, reflecting specific properties of the networks. We also determine specific properties of eigenstates of the Google matrix, including the PageRank. The fidelity of the PageRank is proposed as a characterization of its stability.

PubMed Disclaimer

Similar articles

  • Google matrix, dynamical attractors, and Ulam networks.
    Shepelyansky DL, Zhirov OV. Shepelyansky DL, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Mar;81(3 Pt 2):036213. doi: 10.1103/PhysRevE.81.036213. Epub 2010 Mar 16. Phys Rev E Stat Nonlin Soft Matter Phys. 2010. PMID: 20365838
  • Delocalization transition for the Google matrix.
    Giraud O, Georgeot B, Shepelyansky DL. Giraud O, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Aug;80(2 Pt 2):026107. doi: 10.1103/PhysRevE.80.026107. Epub 2009 Aug 7. Phys Rev E Stat Nonlin Soft Matter Phys. 2009. PMID: 19792200
  • Google matrix and Ulam networks of intermittency maps.
    Ermann L, Shepelyansky DL. Ermann L, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Mar;81(3 Pt 2):036221. doi: 10.1103/PhysRevE.81.036221. Epub 2010 Mar 30. Phys Rev E Stat Nonlin Soft Matter Phys. 2010. PMID: 20365846
  • PageRank and rank-reversal dependence on the damping factor.
    Son SW, Christensen C, Grassberger P, Paczuski M. Son SW, et al. Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Dec;86(6 Pt 2):066104. doi: 10.1103/PhysRevE.86.066104. Epub 2012 Dec 5. Phys Rev E Stat Nonlin Soft Matter Phys. 2012. PMID: 23368001
  • Medical literature search dot com.
    Jain V, Raut DK. Jain V, et al. Indian J Dermatol Venereol Leprol. 2011 Mar-Apr;77(2):135-40. doi: 10.4103/0378-6323.77451. Indian J Dermatol Venereol Leprol. 2011. PMID: 21393941 Review.
See all similar articles

Cited by